Birthday Paradox Simulation in C++ The birthday paradox, states that given a gro

Question

Birthday Paradox Simulation in C++
The birthday paradox, states that given a group of 23 (or more) randomly chosen people, the probability is more than 50% that at least two of them will have the same birthday.
Your task is to use simulation to corroborate the mathematical analysis.
Algorithm:Include the following libraries:

Input (and echo to the output):the number of times to run the simulationa non-negative integer seed value to be used as the input parameter for srand().

Repeat the following simulation the number of times specified by the input:Initialize a 365 (no leap day) element Boolean array to all false.

Declare and initialize a 365 element integer frequency array.Randomly mark birthdays (true) in the 365 element Boolean array until there's a duplicate. Every time there's not a duplicate birthday, increment the frequency array element whose index is the current number of unmatched birthdays.

When there is a duplicate, break out of the loop.When finished, store, in a new (double) array, the ratio of each value in the frequency array to the total number of runs.

This value will be a the simulated probability of not-matching for that many birthdays.In another array of the same size and type, store the theoretical probability of not-matching. ( N = number of birthdays not-matching) computed via the relations:The probability that 0 or 1 birthday won't match is 1.The probability that 2 birthdays won't match is (1 - 1/365) = (1 - ({N=2} - 1)/365) = P(2).The probability that 3 birthdays won't match is (1 - 1/365)*(1 - 2/365) = P(2)*(1 - ({N=3} -1)/365).

The probability that N > 0 birthdays won't match is P(N - 1)*(1 - (N -1)/365).output a table where for each row:

column 1 is the number of birthdays not-matching (starting with 2),

column 2 is the respective theoretical probabilitycolumn 3 is the respective simulated probability

column 4 is the respective absolute error {theoretical - simulated}

column 5 is the respective relative error {fabs((theoretical - simulated) / theoretical)}

(You'll need to use the following I/O manipulators: scientific, setw(), setprecision())

Use the following function to compute a random integer in the interval [0, bound): int irand2bound(int bound) { return static_cast( rand() / (RAND_MAX + 1.0) * bound ); }

output looks like this:

etc

help will be appreciated. I'm really struggling lol.

Explanation / Answer

include <iostream>
#include <cmath>
#include <cstdlib>
#include <iomanip>
#include <ctime>
using namespace std;

int count;
float percentcalculate;
float percentrandom;
float percentdiff;
int DAYS = 365;
int TESTCOUNT = 5000;
int people;
int i;
int test;

void main ()

{
cout << "this is the birthday paradox program" << endl;
cout << "this determines, from 2 - 50 people" << endl;
cout << "the observed and actual probability" << endl;
cout << "of any of those 2 people to share the same birthday" << endl;
cout << "going off of only month and day" << endl;
cout << "people" ;
cout.width (10);
cout << "ob. prob.";
cout.width (10);
cout << "ac. prob.";
cout.width (10);
cout << "percent diff" << endl;

for (count = 2; count <=50; count ++);
{
int people = count;
for (test = 1; test <= TESTCOUNT; test ++);
{
int birthday [count];
birthday [count] = rand () % 365 + 1;
if (birthday [count] = 0
{
birthday = 1;
}
else if (birthday [count] = 1)
samecount ++;
}
percentrandom = ;
percentcalculate = ;
percentdiff = abs(percentrandom - percentcalculate) * 100;
cout << people;
cout.width(10);
cout << percentrandom;
cout.width(10);
cout << percentcalculate;
cout.width(10);
cout << percentdiff << endl;
count++;
}
}



pgm2;

's called a paradox because at first glance it seems counterintuitive that there's a 50% of two people in a group of 23 people sharing the same birthday, rather than the expected probability of 6.297%. The key is that we're not asking for the probability of someone having one particular birthday.

[code]
#include <iostream>

int main(){
std::cout <<"Hello, World! ";
}
[/code]
becomes

  1  2  3  4  5  

  #include <iostream>    int main(){      std::cout <<"Hello, World! ";  }  

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